The unions are seeking to replace concessions made during the 2003 restructuring that kept the airline out of bankruptcy. But federal law makes it hard for airline workers to strike. Even if the mediation board gives unions the go-ahead, the president can still block a strike.

"We don't want to have to strike. I was elected to get a contract and I'm going to do everything I can to get that done. If this helps, then we're on board," said Laura Glading, president of the APFA.

"The company continues to believe that a negotiated agreement is the best solution for our employees, our company and those who depend on us every day – and that there is a significant risk that any other option could lead to an unsatisfactory outcome for both our APFA and TWU-represented employees and for American," said Missy Latham, with American Airlines. "The company is committed to reaching new contracts with the unions that provide competitive pay and benefits and a good career for our employees and yet allow the airline to compete successfully."

The TWU also said that American Airlines and American Eagle will be treated independently and not "lumped" together. In other words, the NMB could elect to release or deny either party at their discretion, according to James Horowitz, spokesperson for the TWU.

"The company negotiating teams remain focused and are ready to get back to work at the table once the NMB sets dates to reconvene the parties," said Latham.

Both unions asked the NMB in March to declare the talks with the airline a stalemate.

NBCDFW's Ken Kalthoff contributed to this report.

Shares of American's parent AMR Corp. are up 31 cents, or 3.5 percent, at $9.06 in afternoon trading